In the spirit of [1]} we have attempted to provide a constructive proof, and hope that the results here presented will enable the implementation of new phylogenetic methods. There are several options for such an implementation. [2]} provide an algorithm for directly applying the concepts in [1]} to learn the full model parameters using spectral methods. It would be relatively straightforward to adapt that approach to the proof to Theorem REF . Alternatively, progress is being made towards fitting models that are heterogeneous across lineages [4]}, [5]}. These methods could be adapted to our setting. Also, the method of [6]} where a homogeneous process is fitted to the whole tree would be trivial to implement for a strand symmetric process, but could be done with a solid theoretical basis and new insight into the limits of inference of such a model.
